Move center of radial anisotropic to center of object
You could remap center of anisotropic shading to an object (this could be an Empty); use Texture Coordinates node for that:



With that, once you move the empty, center of the anisotropic shading will move as well. Note that this can even change the axis of the shading; however controling may be not as convenient as if using Tangent node to change the axis.